Explainable artificial intelligence in medical imaging is currently dominated by post-hoc tools that rationalise the decisions of otherwise opaque deep networks, without providing, most of the time, a robust and transparent decision rule. This paper presents an interpretable mathematical model for pneumonia detection in pediatric chest radiographs. We propose a symbolic classification framework that evolves a non-linear closed-form diagnostic formula directly from a compact set of clinically grounded radiomic markers, including entropy, solidity, and fractal dimension. To our knowledge, this is the first single-formula symbolic classifier reported for pediatric pneumonia detection on the specific dataset. The symbolic classifier achieved 87% accuracy and AUC = 0.93 under 10-fold cross-validation. When the selected closed-form equation was applied to the filtered independent hold-out test set, it achieved 79.1% accuracy and AUC = 0.89. The equation has been further validated and re-calibrated on an independently acquired external dataset. With a parameter count several orders of magnitude smaller than that of competing deep learning models, and an auditable closed-form expression, the proposed model provides a lightweight, transparent baseline suited to resource-constrained inference and regulatory audit. The proposed framework can be applied in complementary ways to existing deep learning pipelines, as an intrinsically interpretable alternative that broadens the methodological repertoire for clinically transparent diagnosis.

In this paper, we investigate the application of Symbolic Regression (SR) to develop wall models for fully developed, pressure-driven turbulent channel flows. Using high quality Direct Numerical Simulation (DNS) data for training, we compare SR-generated models against classical composite wall law models. Two distinct SR strategies are evaluated: a global model (SRW) trained across all Reynolds numbers, and Reynolds-specific models (SRWRe) trained individually for each case. In parallel, a tree-based machine learning model, which is accurate but not interpretable, is employed as a high-accuracy benchmark, providing a baseline against which all other models are compared. Our results demonstrate that SR-derived models adhere to physical constraints and match the accuracy of high-resolution CFD while remaining computationally efficient, outperforming classical composite wall law models in the complex buffer and transition regions. Furthermore, we analyze the ability of these expressions to extrapolate beyond their training conditions, specifically for higher Reynolds number flows. This is a critical step toward developing robust wall functions for industrial-scale CFD, as it evaluates whether the SR-derived models have captured universal scaling laws of wall turbulence rather than merely overfitting to the specific, lower Reynolds number regimes where DNS data is currently accessible. The resulting expressions highlight the potential of SR to bridge the gap between data-driven approaches and classical theory, providing a transparent and explainable framework for future turbulence closure modeling and near-wall physics exploration.

Atomic-scale simulations, such as molecular dynamics (MD), have undergone a rapid evolution during the past decades, leading to their broad adoption in various scientific and engineering fields, where they have unveiled hidden phenomena otherwise inaccessible through experiments. In recent years, the integration of machine learning (ML), either as a post-processing tool or embedded directly in a hybrid manner to the simulation workflow, has further enhanced the predictive power of MD by improving accuracy, reducing computational costs, and uncovering patterns in high-dimensional data. This review investigates the integration of MD with ML by identifying existing approaches for their combination within popular simulation platforms. It incorporates an analysis of research trends from 2020 to 2025 based on Scopus-indexed publications. By synthesizing recent developments and highlighting ongoing challenges, this review aims to guide future efforts in exploiting the full potential of MD/ML integration across scientific and engineering disciplines, such as computational chemistry and physics, biomolecular engineering, medicine, soft matter physics, materials science and nanotechnology.

The application of Machine Learning (ML)-based techniques was explored to create a fully predictive framework for estimating the thermal conductivity of multi-component mixtures containing hydrocarbons and oxygenated compounds. The study followed these steps: (i) three datasets were constructed using experimental thermal conductivity data for both pure compounds and binary mixtures available in the literature, (ii) Symbolic regression was then applied to generate mixing rules considering five independent data manipulation strategies, (iii) new quantitative structure-property relationship (QSPR) models were developed and benchmarked against work previously published in the literature, and then (iv) QSPR models were used to power mixing rules generated with symbolic regression to predict thermal conductivity values of binary mixtures. A mixing rule was then designed to propose a potential extension to multi-component – two or more components – mixtures. Validation of the latter mixing rule powered with QSPR predictions was performed considering a set of ternary and quaternary mixtures. Finally, the approach was applied to predict the thermal conductivity of four jet fuel samples at different temperatures and atmospheric pressures, resulting in a mean absolute error of 2.9%. Performed comparative analysis confirmed that the developed methodology is effective across a wide range of liquid hydrocarbon and oxygenated mixtures.

This paper employs Physics-Informed Neural Networks (PINNs) for the reconstruction and modelling of mean velocity profiles in fully developed turbulent channel flow over a high friction Reynolds number (Reτ). The network is trained with a high-fidelity Direct Numerical Simulation (DNS) dataset from channel flows, for Reτ=395–4186, and can extrapolate up to Reτ = 10,049. The model predicts the mean velocity in terms of the inner-law variables, u+, across Reynolds numbers using the inputs η=y+/Reτ and Reτ. A key novelty is the simultaneous optimisation of the network weights alongside two fundamental turbulence parameters, i.e., the von Kármán constant (κ) and the van Driest damping constant (A+), allowing the PINN to autonomously calibrate the near-wall damping and log-law scaling directly from the physics-augmented loss function. The model performance is evaluated using profile-based metrics (R2, mean square and absolute error) and integrated quantities (V¯+, Reb, and the skin-friction coefficient Cf), with comparisons against DNS-integrated friction values and classical theoretical values. The resulting hybrid framework offers a promising foundation for real-time digital twins and the acceleration of Computational Fluid Dynamics (CFD) solvers in canonical wall-bounded flows. By establishing a physically grounded connection between sparse data and structural constraints, these models enable accurate extrapolation into high Reynolds number regimes where the computational costs of traditional high-fidelity simulations are otherwise prohibitive.

A machine learning approach, namely symbolic regression (SR), is applied in the stellarator Wendelstein 7-X (W7-X), to investigate the effect of six plasma parameters (line integrated electron density, heating power, toroidal plasma current, fraction of radiated power, core and edge ion temperatures) on the sub-divertor neutral gas pressure. Based on the data from the OP1.2b experimental campaign, closed-form expressions of the neutral gas pressure in terms of the plasma parameters are deduced for the standard, high iota and high mirror magnetic configurations at three different ports of the exhaust system. While common regression schemes assume a predetermined functional form, SR autonomously discovers, via genetic programming, the functional structure of the model, purely from data. In all cases, the optimized data driven SR framework clearly points out that, in estimating the neutral gas pressure, the most dominant parameters are the electron density and the heating power, while the remaining plasma parameters have minor impact, at least from the statistical point of view and may not be included in the correlations. Balancing model generality, complexity(COMP) and accuracy for all considered magnetic configurations and ports, the proposed closed form expressions contain only the product of electron density and heating power raised at some powers, times a constant. The proposed two-parameter symbolic expressions, exhibiting low COMP and excellent accuracy metrics, provide a practical and analytical tool for the acceleration of the neutral gas pressure calculations, that are otherwise computationally very expensive and for the overall performance assessment of the W7-X exhaust system. They may also contribute to more efficient experimental design and operation. performance assessment of the W7-X exhaust system. They may also contribute to more efficient experimental design and operation.

This paper examines the temperature distribution in a closed, rectangular room equipped with an air conditioning system, employing a computational fluid dynamics model to simulate a virtual thermal camera that captures detailed temperature snapshots. A super-resolution framework enhances the postprocessing of these results. Specifically, convolutional neural networks, trained on simulation data, are used to accurately model temperature fields' high-resolution spatial and temporal evolution. The model demonstrates strong performance by accurately reconstructing temperature profiles from low-resolution inputs obtained from filtering data obtained using high-resolution numerical simulations, with quantitative metrics indicating acceptable accuracy for resolutions reduced by up to 50 times. This effectively aligns with ground truth profiles under various conditions. These results underscore the super-resolution model's potential to transform environmental monitoring in smart buildings and complex structures by generating high-resolution thermal maps from low-resolution cameras or limited sensor input. This approach offers a fast, cost-effective, and reliable method for accurately modeling thermal dynamics within the turbulent flow environments of interior spaces.

Fluid mechanics research is currently undergoing a significant transformation, driven by the integration of advanced computational intelligence [...]

This study presents a novel deep learning framework aimed at achieving super-resolution of velocity fields within turbulent channel flows across various wall-normal positions. The model excels at reconstructing high-resolution flow fields from low-resolution data, with an emphasis on accurately capturing spatial structures and spectral energy distributions. Input data are generated through fine-grid large eddy simulations, employing a data-driven approach. The model's efficacy is evaluated using standard image quality metrics, including peak signal-to-noise ratio, structural similarity index measure, root mean square error, mean absolute error, good pixel percentage, as well as spectral analyses to encapsulate the complex dynamics of turbulent flow physics. The findings demonstrate substantial correlations between model performance and wall-normal location. Specifically, the model performs superior in regions distal from the channel wall but faces challenges in accurately recovering small-scale turbulent structures near the boundary layer.

This research investigates high school students’ understanding of mathematical, physical, and biological systems exhibiting Fractal structures, with the aim of enhancing their comprehension of nature’s intrinsic complexity. The research explores the pedagogical integration of Fractal Geometry, emphasizing key concepts such as scaling, self-similarity, and Fractal dimension, and examines their applications in both mathematical and natural systems. The research employs an instructional intervention designed to evaluate students’ conceptual understanding, the characterization of Fractal sets and systems, and the impact on their motivation for learning Natural Sciences. Both qualitative and quantitative methods were used, including pre- and post-test questionnaires, worksheets, and statistical analyses. Nonparametric tests (Wilcoxon Signed-Rank and Mann–Whitney U) were used due to nonnormal data distributions, and the reliability and validity of the instruments were verified. The results reveal that Students’ initial alternative conceptions shifted toward scientifically accepted ideas, and their motivation for the Natural Sciences increased substantially. Field-based activities involving authentic Fractal structures proved particularly effective in engaging learners, fostering active participation, retention, and meaningful knowledge construction. The research demonstrates that the pedagogical use of Fractal Geometry provides an innovative and effective approach to teaching complex scientific phenomena. It bridges theoretical concepts and practical experience, enhances critical and creative thinking, and contributes to scientific literacy, offering new tools for interdisciplinary education and for teaching the natural world.

High-resolution data are essential for analysing turbulent flows, yet direct numerical simulations are often computationally prohibitive. Super-resolution based on deep learning (DL) offers a promising alternative for reconstructing high-fidelity fields from coarse data. This study introduces and validates a novel hybrid framework that combines classical interpolation with a convolutional neural network (CNN) to perform super-resolution on two-dimensional turbulent flow fields. The architecture is designed to be computationally efficient and physically consistent, leveraging interpolation as a method to assist in simplifying the reconstruction task for the DL model. We evaluated the framework on three distinct turbulent flow cases-interior room airflow, sudden expansion corner flow, and turbulent channel flow-using data from implicit Large Eddy Simulations. The performance was benchmarked against both standalone interpolation methods and conventional CNN-only architectures. Results demonstrate that the hybrid approach provides superior reconstruction accuracy, as quantified by numerical measures including peak signal-to-noise ratio and the structural similarity index. Furthermore, we validate the physical consistency of the reconstructed fields by analysing their energy spectra and turbulence probability density functions, confirming that the model faithfully reproduces the essential characteristics of turbulent flow physics. This work presents a practical and effective tool for generating high-quality turbulence data at a fraction of the computational cost required by traditional methods.

Machine Learning methods are exploited to extract a universal approach for self-diffusion coefficient calculation in molecular fluids. Analytical expressions are derived through symbolic regression for fluids both in bulk and confined nanochannels. The symbolic regression framework is trained on simulation data from molecular dynamics and correlates the values of the self-diffusion coefficients with macroscopic properties, such as density, temperature, and the width of confinement. New expressions are derived for nine different molecular fluids, while an all-fluid universal equation is extracted to capture molecular behavior as well. In such a way, a highly computationally demanding property is predicted by easy-to-define macroscopic parameters, bypassing traditional numerical methods based on mean squared displacement and autocorrelation functions at the atomistic level. To achieve generalizability and interpretability, simple symbolic expressions are selected from a pool of genetic programming-derived equations. The obtained expressions present physical consistency, and they are discussed in terms of explainability. The accurate prediction of the self-diffusion coefficient both in bulk and confined systems is important for advancing the fundamental understanding of fluid behavior and leading the design of nanoscale confinement devices containing real molecular fluids.

This paper implements a spatiotemporal neural network architecture based on the U-Net prototype with four branches, UBranch, to perform both spatial reconstruction and temporal forecasting of flow fields. A high-speed turbulent flow featuring shock-wave turbulent boundary layer interaction is utilized to demonstrate the forecasting in two-dimensional flow frames. The main elements of UBranch consist of convolutional neural networks, which are fast and lightweight for such functions, in a form that bypasses the use of complex and time-consuming long-short-term memory networks. The proposed model can provide the following four future time frames when fed with a sequence of two-dimensional flow images with reasonable accuracy and low root mean square error, and, in parallel, it can indicate the maximum pressure points, which is of primary importance for shock-wave turbulent boundary layer interaction. Apart from the temporal operation, UBranch can also perform spatial super-resolution tasks, reconstructing a low-resolution image to a finer field with increased accuracy. Calculated peak signal-to-noise ratios reach 29.0 for spatiotemporal and 35.0 for spatial-only tasks.

Kinetic theory and modeling have been proven extremely suitable in computing the flow rates in rarefied gas pipe flows, but they are computationally expensive and more importantly not practical in design and optimization of micro- and vacuum systems. In an effort to reduce the computational cost and improve accessibility when dealing with such systems, two efficient methods are employed by leveraging machine learning (ML). More specifically, random forest regression (RFR) and symbolic regression (SR) have been adopted, suggesting a framework capable of extracting numerical predictions and analytical equations, respectively, exclusively derived from data. The database of the reduced flow rates W used in the current ML framework has been obtained using kinetic modeling and it refers to nonlinear flows through circular tubes (tube length over radius l ∈ [0,5] and downstream over upstream pressure p ∈ [0,0.9] ) in a very wide range of the gas rarefaction parameter δ∈ [0,10^3] . The accuracy of both RFR and SR models is assessed using statistical metrics, as well as the relative error between the ML predictions and the kinetic database. The predictions obtained by RFR show very good fit on the simulation data, having a maximum absolute relative error of less than 12.5% . Various expressions of the form of W=W(p,l,δ ) with different accuracy and complexity are acquired from SR. The proposed equation, valid in the whole range of the relevant parameters, exhibits a maximum absolute relative error less than 17% . To further improve the accuracy, the dataset is divided into three subsets in terms of δ and one SR-based closed-form expression of each subset is proposed, achieving a maximum absolute relative error smaller than 9% . Very good performance of all proposed equations is observed, as indicated by the obtained accuracy measures. Overall, the present ML-predicted data may be very useful in gaseous microfluidics and vacuum technology for engineering purposes.

The success of deep learning models in fluid dynamics applications will depend on their ability to handle sparse and noisy data accurately. This paper concerns the development of a deep learning model for reconstructing turbulent flow images from low-resolution counterparts encompassing noise. The flow is incompressible through a symmetric, sudden expansion featuring bifurcation, instabilities, and turbulence. The deep learning model is based on convolutional neural networks, in a high-performance, lightweight architecture. The training is performed by finding correlations between high- and low-resolution two-dimensional images. The study also investigates how to remove noise from flow images after training the model with high-resolution and noisy images. In such flow images, the turbulent velocity field is represented by significant color variations. The model's peak signal-to-noise ratio is 45, one of the largest achieved for such problems. Fine-grained resolution can be achieved using sparse data at a fraction of the time required by large-eddy and direct numerical simulation methods. Considering its accuracy and lightweight architecture, the proposed model provides an alternative when repetitive experiments are complex and only a small amount of noisy data is available.

Fluid mechanics’ simulations are widely incorporated in place of expensive and complex experiments, providing accurate property fields in a dense grid fashion. It is a fact that experimental measurements due to their discrete and, most of the times, sparse data representation, cannot fully define velocity, pressure, temperature, vorticity, which are common properties of interest, especially in turbulent flows. The need to upscale flow features from coarse-grained data has been successfully addressed during the past years with aid of novel artificial intelligence -based methods. This upscaling refers either to sparse experimental data or to coarse simulation data, bypassing computationally intensive classical direct numerical simulations. This study presents a deep learning approach that accepts low resolution vorticity fields, from an open channel flow simulation, and reconstructs the field to resemble a fine grid result. This super resolution approach shows that reconstruction is possible as long as the network training is performed using pairs of low/high resolution fields. The proposed model is based on the U-Net architecture and is investigated over the effect of the resolution scale factor of the input images.

The integration of machine learning (ML) techniques into industrial and manufacturing applications has seen great growth in recent years. Various numerical and analytical models have been proposed, based either on experimental results or simulation results, and have helped to understand phenomena that take place during the life cycle of a material. In this direction, a large experimental data set to determine the compressive strength of FRP (FRP) prestressed concrete specimens has been used as a basis in this work. The obtained measurements are correlated with the mechanical and structural properties of the material and fed into a ML model. The model is trained on the experimental values ​​and can provide predictions for conditions within or outside the value range of the input data. Various MLalgorithms are implemented and studied for their prediction accuracy, and the results show that ML can be an important computational tool, which can act as a complement to expensive experiments or time-consuming simulations in engineering sciences.

Upscaling flow features from coarse-grained data is paramount for extensively utilizing computational physics methods across complex flow, acoustics, and aeroelastic environments where direct numerical simulations are computationally expensive. This study presents a deep learning flow image model for upscaling turbulent flow images from coarse-grained simulation data of supersonic shock wave–turbulent boundary layer interaction. It is shown for the first time that super-resolution can be achieved using only the coarsest-grained data as long as the deep learning training is performed using hundreds of fine-grained data. The unsteady pressure data are used in training due to their importance in aeroelasticity and acoustic fatigue occurring on aerospace structures. The effect on the number of images and their resolution features used in training, validation, and prediction is investigated regarding the model accuracy obtained. It is shown that the deep learning super-resolution model provides accurate spectra results, thus confirming the approach's effectiveness.

The viscosity and thermal conductivity coefficients of the Lennard-Jones fluid are extracted through symbolic regression (SR) techniques from data derived from simulations at the atomic scale. This data-oriented approach provides closed form relations that achieve fine accuracy when compared to well-established theoretical, empirical, or approximate equations, fully transparent, with small complexity and high interpretability. The novelty is further outlined by suggesting analytical expressions for estimating fluid transport properties across the whole phase space, from a dilute gas to a dense liquid, by considering only two macroscopic properties (density and temperature). In such expressions, the underlying physical mechanisms are reflected, while, at the same time, it can be a computationally efficient alternative to costly in time and size first principle and/or molecular dynamics simulations.

Data science and machine learning (ML) techniques are employed to shed light into the molecular mechanisms that affect fluid-transport properties at the nanoscale. Viscosity and thermal conductivity values of four basic monoatomic elements, namely, argon, krypton, nitrogen, and oxygen, are gathered from experimental and simulation data in the literature and constitute a primary database for further investigation. The data refers to a wide pressure–temperature (P-T) phase space, covering fluid states from gas to liquid and supercritical. The database is enriched with new simulation data extracted from our equilibrium molecular dynamics (MD) simulations. A machine learning (ML) framework with ensemble, classical, kernel-based, and stacked algorithmic techniques is also constructed to function in parallel with the MD model, trained by existing data and predicting the values of new phase space points. In terms of algorithmic performance, it is shown that the stacked and tree-based ML models have given the most accurate results for all elements and can be excellent choices for small to medium-sized datasets. In such a way, a twofold computational scheme is constructed, functioning as a computationally inexpensive route that achieves high accuracy, aiming to replace costly experiments and simulations, when feasible.